The Scaling Limit of the (∇ + Δ) -Model

Alessandra Cipriani*, Biltu Dan, Rajat Subhra Hazra

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


In this article we study the scaling limit of the interface model on Zd where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic methods, in finite volume we rely on some discrete PDE techniques involving finite-difference approximation of elliptic boundary value problems.

Original languageEnglish
Article number39
Pages (from-to)1-23
Number of pages23
JournalJournal of Statistical Physics
Issue number2
Publication statusPublished - 2021


  • Gaussian free field
  • Membrane model
  • Mixed model
  • Random interface
  • Scaling limit


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